Centrifugal processing devices have been used to separate liquids and/or to finish or otherwise smooth surfaces of different objects. Some of these processing devices have an outer vessel and a turret within the outer vessel that is rotated about the axis of the outer vessel. The turret includes at least one inner vessel that rotates about its own axis as the turret rotates about the axis of the outer vessel. In particular, a frictional force between the inner vessel and the outer vessel causes the inner vessel to rotate in a rotational direction that is opposite the rotational direction of the turret as the turret is rotated about the outer vessels axis. The contents of the inner vessels of such processing devices are subjected to an acceleration several hundred times that associated with gravity (“g”). While these devices are useful for finishing objects and/or separating liquids, their utility for applications such as processing particulate materials such as pharmaceuticals could be improved by increasing the acceleration to which their contents are subjected. Furthermore, there is a need for devices of this type in which substantially the same forces and accelerations act on the contents of the mixing device.